NEW YORK -- The Houston Texans' asking price for the No. 1 overall pick in the NFL draft, for at least two inquiring clubs, is three first-round picks at a minimum, according to NFL Media insider Ian Rapoport.

With former South Carolina star Jadeveon Clowney the object of desire, Houston Texans general manager Rick Smith is seeking premium value for the pass rusher. Rapoport reports a swap of first-round picks Thursday night, plus two future first-rounders, is the demand.

The Texans aren't sold on Clowney as the No. 1 pick. "He doesn't appear to be a fit for their defense," Rapoport said Wednesday on Total Access, adding that effort issues aren't a concern for the team.

So who would buy?

It's an especially steep price tag for a team like the Atlanta Falcons, who are among the clubs most interested in Clowney. They would only be moving five spots ahead from the No. 6 position. In 2011, Atlanta spent two first-rounders, a second and two fourths to move up 21 spots to No. 6 in a stunning first-day trade with the Cleveland Browns to draft wide receiver Julio Jones.

John McClain of the Houston Chronicle reported via Twitter that the Texans would also like to acquire second- and third-round picks this year in such a deal, but with just one future first-round pick (2015). That asking price could be better-aligned with a club seeking to move ahead from a higher position, such as Atlanta.

Meanwhile, Clowney is soaking up draft week in the Big Apple and letting the executives worry about trades. Wednesday night, he made an appearance on The Tonight Show and got to clock host Jimmy Fallon in the 40-yard dash.

Running in a suit and dress shoes, Fallon didn't benefit from optimum conditions. But he's not worth trading up for, either.